login
Number of permutations of {1,2,3,...,n^2} where no multiples of n are consecutive.
0

%I #11 Aug 16 2019 15:17:02

%S 1,12,151200,8219667456000,5940854755726373683200000,

%T 140616461430273488287535887653273600000000,

%U 228186389638197777421971812759876473627903014249431040000000000

%N Number of permutations of {1,2,3,...,n^2} where no multiples of n are consecutive.

%C limit{n->oo} a(n)/(n^2)! = 1/e.

%F a(n) = (n^2 -n)! *(n^2 -n +1)! /(n^2 -2*n +1)!.

%e If n = 2, we have the permutations:

%e 1,2,3,4; 1,4,3,2; 3,2,1,4; 3,4,1,2;

%e 2,1,3,4; 4,1,3,2; 2,3,1,4; 4,3,1,2;

%e 2,1,4,3; 4,1,2,3; 2,3,4,1; 4,3,2,1

%e (no multiples of 2 are adjacent in any of the permutations). So a(2) = 12.

%p a:=n->(n^2-n)!*(n^2-n+1)!/(n^2-2*n +1)!: seq(a(n),n=1..8); # _Emeric Deutsch_, Aug 03 2005

%K nonn

%O 1,2

%A _Leroy Quet_, Jan 11 2005

%E More terms from _Emeric Deutsch_, Aug 03 2005